An estimate for weighted Hilbert transform via square functions

Authors:
S. Petermichl and S. Pott

Journal:
Trans. Amer. Math. Soc. **354** (2002), 1699-1703

MSC (1991):
Primary 42A50; Secondary 42A61

Published electronically:
October 26, 2001

MathSciNet review:
1873024

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the norm of the Hilbert transform as an operator on the weighted space is bounded by a constant multiple of the power of the constant of , in other words by . We also give a short proof for sharp upper and lower bounds for the dyadic square function.

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Additional Information

**S. Petermichl**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027

Address at time of publication:
Institute of Advanced Studies, Princeton, New Jersey 08540

Email:
stefanie@math.msu.edu

**S. Pott**

Affiliation:
Department of Mathematics, University of York, York YO10 5DD, UK

Email:
sp23@york.ac.uk

DOI:
http://dx.doi.org/10.1090/S0002-9947-01-02938-5

Keywords:
Weighted norm inequalities,
square function,
Hilbert transform

Received by editor(s):
August 15, 2001

Published electronically:
October 26, 2001

Additional Notes:
The second author gratefully acknowledges support by EPSRC and thanks the Mathematics Department at MSU for its hospitality

Article copyright:
© Copyright 2001
American Mathematical Society